Calendars – keeping track of time
Box 1 | Zeroing in on nothing
In the middle of the 6th century, Pope St John I asked scholar Dionysius Exiguus to calculate the dates on which Easter would fall in future years. When compiling the dates, Dionysius decided to abandon the numbering system for calendars that counted years from the beginning of the reign of the Roman Emperor, Diocletian. He replaced it with a numbering system that started with the birth of Christ, which he called the year 1, probably because there was no zero in the system of Roman numerals, in which I meant 1, V meant 5, X meant 10 and C meant 100.
You may be surprised to learn that zero is one of the most important concepts in mathematics and has a long and controversial history. What makes a zero so special?
Zero as a place-holder
One of zero's many useful functions is as a ‘place-holder’. For example, in the number 600, the zero immediately to the right of 6 informs us that the ‘tens’ column is empty; the zero to the right of that tells us that the ‘units’ column is also empty. The only column that has any values in it is the ‘hundreds’ column. But if we did not somehow indicate that the two right-hand columns were empty we would write ‘600’ as ‘6’, which is not the number that we mean.
Because zero means ‘nothing’, it is a concept that took a long time to be accepted. Historians argue about who first came to terms with it, although they seem to agree that the first recorded use of it was as a place-holder in the ancient civilisation of Babylon around 300 BCE. But it took much longer before it became a meaningful mathematical concept. Part of the reason was an apparent problem of logic: how could ‘nothing’ have any meaning?
Zero as a symbol
Zero really came into its own via India, where it first gained recognition perhaps 1500 years ago. Various words with meanings similar to ‘nothing’ became incorporated into the poems of Hindu mathematicians (yes, they wrote their mathematical problems in verse). For example, sunya meant void, kha meant sky and akasa meant space. Eventually, as the verse evolved to something closer to the way we write our maths today, a dot or open circle came to symbolise zero in mathematical equations.
Solving quadratic equations
The importance of zero in modern mathematics can be illustrated by a simple – although not so modern – example. In the late 1500s, a Scottish baron by the name of John Napier found a way of solving quadratic equations of the form:
x2 + 2x = 24 (Equation 1)
The aim, of course, is to work out the value of x. Napier realised that he could rewrite such an equation as follows:
x2 + 2x – 24 = 0 (Equation 2)
The left-hand side of the equation, in turn, could be rewritten to give:
(x – 4)(x + 6) = 0 (Equation 3)
For the product of two values to equal zero, as in Equation 3, one of them must be zero. So either (x – 4) equals zero (thus, x = 4), or (x + 6) equals zero (thus, x = –6). This way of solving quadratic equations is now commonplace in schools – but its discovery helped give mathematics the power to solve real-world problems such as those encountered in engineering.
Related sites
Zero (The Atlantic Monthly, July 1997)
A history of zero (School of Mathematics and Computational Sciences, University of St Andrews, UK)
Zero for children
(Ask Dr. Math, Swarthmore College, USA)
History of zero and place value
(Ask Dr. Math, Swarthmore College, USA)
Zero in four dimensions: Cultural, historical, mathematical, and psychological perspectives (University of Baltimore, USA)
Page updated August 2002.